Optimal actuator design for linear systems with multiplicative noise.

Mohamed Ali Belabbas, Artur Kirkoryan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper addresses optimal actuator design for linear systems with process noise. It is well-known that the control that minimizes a quadratic cost in the state and control for a system with linear dynamics corrupted by additive Gaussian noise is of feedback type and its design depends on the solution of an associated Riccati equation. We consider here the case where the noise is multiplicative, by which we mean that its intensity is dependent on the state. We show how to derive the actuator that minimizes a linear quadratic cost. The solution requires to optimize a function defined on a manifold of low rank matrices; we provide a gradient descent algorithm to perform this optimization and show that this gradient descent converges to the global minimum almost surely.

Original languageEnglish (US)
Title of host publication2018 European Control Conference, ECC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2726-2731
Number of pages6
ISBN (Electronic)9783952426982
DOIs
StatePublished - Nov 27 2018
Event16th European Control Conference, ECC 2018 - Limassol, Cyprus
Duration: Jun 12 2018Jun 15 2018

Publication series

Name2018 European Control Conference, ECC 2018

Other

Other16th European Control Conference, ECC 2018
CountryCyprus
CityLimassol
Period6/12/186/15/18

Fingerprint

Multiplicative Noise
Gradient Descent
Linear systems
Actuator
Actuators
Linear Systems
Minimise
Low-rank Matrices
Descent Algorithm
Riccati equations
Gradient Algorithm
Gaussian Noise
Costs
Global Minimum
Riccati Equation
Multiplicative
Optimise
Converge
Feedback
Optimization

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization

Cite this

Belabbas, M. A., & Kirkoryan, A. (2018). Optimal actuator design for linear systems with multiplicative noise. In 2018 European Control Conference, ECC 2018 (pp. 2726-2731). [8550344] (2018 European Control Conference, ECC 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ECC.2018.8550344

Optimal actuator design for linear systems with multiplicative noise. / Belabbas, Mohamed Ali; Kirkoryan, Artur.

2018 European Control Conference, ECC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 2726-2731 8550344 (2018 European Control Conference, ECC 2018).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Belabbas, MA & Kirkoryan, A 2018, Optimal actuator design for linear systems with multiplicative noise. in 2018 European Control Conference, ECC 2018., 8550344, 2018 European Control Conference, ECC 2018, Institute of Electrical and Electronics Engineers Inc., pp. 2726-2731, 16th European Control Conference, ECC 2018, Limassol, Cyprus, 6/12/18. https://doi.org/10.23919/ECC.2018.8550344
Belabbas MA, Kirkoryan A. Optimal actuator design for linear systems with multiplicative noise. In 2018 European Control Conference, ECC 2018. Institute of Electrical and Electronics Engineers Inc. 2018. p. 2726-2731. 8550344. (2018 European Control Conference, ECC 2018). https://doi.org/10.23919/ECC.2018.8550344
Belabbas, Mohamed Ali ; Kirkoryan, Artur. / Optimal actuator design for linear systems with multiplicative noise. 2018 European Control Conference, ECC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 2726-2731 (2018 European Control Conference, ECC 2018).
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